Abstract

Strong scattering properties are obtained for a monolayer of randomly packed polystyrene microspheres. This gives rise to structural colors in transmission. For a sphere diameter between 0.5 and 1 micron, light is mainly scattered in the forward direction. Consequently, in-plane multiple scattering can be neglected when spheres are not too close to each others. This allows one to use a single scattering approximation to reproduce transmission spectra of the system. The film color is dependent on the sphere size, but also on the observation angle. This angular dependant color is reproduced taking into account multiple scattering between spheres. These films can be useful when low reflection is needed.

© 2008 Optical Society of America

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References

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  1. J. Watanabe, K. Okoshi, N. Sano, and S. Edo, "Coloration due to Christiansen Effect in Colloidal Solutions of Amphiphilic Hydroxypropylcellulose," in Structural colors in Biological Systems - Principles and Applications, S. Kinoshita and S. Yoshioka, eds. (Osaka University Press, 2005), pp. 319-327.
  2. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strong scattering media," Nature 368, 436-438 (1994).
    [CrossRef]
  3. Q1. H. Cao, "Random Lasers: development, features and applications," Opt. Photon. News 16, 24-29 (2005).
    [CrossRef]
  4. D. S. Wiersma and A. Lagendijk, "Light diffusion with gain and random lasers," Phys. Rev. E 54, 4256-4265 (1996).
    [CrossRef]
  5. H. Cao, J.Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E.W. Seelig, X. Liu, and R. P. H. Chang, Spatial Confinement of Laser Light in Active Random Media, Phys. Rev. Lett. 84, 5584-5587 (2000).
    [CrossRef] [PubMed]
  6. H. Hattori, "Anti-reflection surface with particle coating deposited by electrostatic attraction," Adv. Mater 13, 51-54 (2001).
    [CrossRef]
  7. T. Serizawa, H. Takeshita, and M. Akashi, "Electrostatic adsorption of polystyrene nanospheres onto the surface of an ultrathin polymer film prepared by using an alternate adsorption technique," Langmuir 14, 4088-4094 (1998).
    [CrossRef]
  8. R. H. Swendsen, "Dynamics of random sequential adsorption," Phys. Rev. A 24, 504-508 (1981).
    [CrossRef]
  9. H.C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  10. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, 1969).
  11. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  12. K. M. Hong, "Multiple scattering of electromagnetic waves by a crowded monolayer of spheres: Application to migration imaging films," J. Opt. Soc. Am. 70, 821-826 (1980).
    [CrossRef]
  13. T. Wriedt, "Electromagnetic Scattering Programs," http://www.iwt-bremen.de/vt/laser/wriedt/index_ns.html.
  14. V. P. Dick, A. P. Ivanov, and V. A. Loiko, "Characteristics of the attenuation of radiation by a monolayer of discrete scatterers," J. Appl. Spectrosc. 47,966-971 (1988).
    [CrossRef]
  15. M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951).
    [CrossRef]

2005 (1)

Q1. H. Cao, "Random Lasers: development, features and applications," Opt. Photon. News 16, 24-29 (2005).
[CrossRef]

2001 (1)

H. Hattori, "Anti-reflection surface with particle coating deposited by electrostatic attraction," Adv. Mater 13, 51-54 (2001).
[CrossRef]

2000 (1)

H. Cao, J.Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E.W. Seelig, X. Liu, and R. P. H. Chang, Spatial Confinement of Laser Light in Active Random Media, Phys. Rev. Lett. 84, 5584-5587 (2000).
[CrossRef] [PubMed]

1998 (1)

T. Serizawa, H. Takeshita, and M. Akashi, "Electrostatic adsorption of polystyrene nanospheres onto the surface of an ultrathin polymer film prepared by using an alternate adsorption technique," Langmuir 14, 4088-4094 (1998).
[CrossRef]

1996 (1)

D. S. Wiersma and A. Lagendijk, "Light diffusion with gain and random lasers," Phys. Rev. E 54, 4256-4265 (1996).
[CrossRef]

1994 (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strong scattering media," Nature 368, 436-438 (1994).
[CrossRef]

1988 (1)

V. P. Dick, A. P. Ivanov, and V. A. Loiko, "Characteristics of the attenuation of radiation by a monolayer of discrete scatterers," J. Appl. Spectrosc. 47,966-971 (1988).
[CrossRef]

1981 (1)

R. H. Swendsen, "Dynamics of random sequential adsorption," Phys. Rev. A 24, 504-508 (1981).
[CrossRef]

1980 (1)

1951 (1)

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951).
[CrossRef]

Adv. Mater (1)

H. Hattori, "Anti-reflection surface with particle coating deposited by electrostatic attraction," Adv. Mater 13, 51-54 (2001).
[CrossRef]

J. Appl. Spectrosc. (1)

V. P. Dick, A. P. Ivanov, and V. A. Loiko, "Characteristics of the attenuation of radiation by a monolayer of discrete scatterers," J. Appl. Spectrosc. 47,966-971 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

Langmuir (1)

T. Serizawa, H. Takeshita, and M. Akashi, "Electrostatic adsorption of polystyrene nanospheres onto the surface of an ultrathin polymer film prepared by using an alternate adsorption technique," Langmuir 14, 4088-4094 (1998).
[CrossRef]

Nature (1)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strong scattering media," Nature 368, 436-438 (1994).
[CrossRef]

Opt. Photon. News (1)

Q1. H. Cao, "Random Lasers: development, features and applications," Opt. Photon. News 16, 24-29 (2005).
[CrossRef]

Phys. Rev. A (1)

R. H. Swendsen, "Dynamics of random sequential adsorption," Phys. Rev. A 24, 504-508 (1981).
[CrossRef]

Phys. Rev. E (1)

D. S. Wiersma and A. Lagendijk, "Light diffusion with gain and random lasers," Phys. Rev. E 54, 4256-4265 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

H. Cao, J.Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E.W. Seelig, X. Liu, and R. P. H. Chang, Spatial Confinement of Laser Light in Active Random Media, Phys. Rev. Lett. 84, 5584-5587 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

M. Lax, "Multiple scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951).
[CrossRef]

Other (5)

J. Watanabe, K. Okoshi, N. Sano, and S. Edo, "Coloration due to Christiansen Effect in Colloidal Solutions of Amphiphilic Hydroxypropylcellulose," in Structural colors in Biological Systems - Principles and Applications, S. Kinoshita and S. Yoshioka, eds. (Osaka University Press, 2005), pp. 319-327.

H.C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, 1969).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

T. Wriedt, "Electromagnetic Scattering Programs," http://www.iwt-bremen.de/vt/laser/wriedt/index_ns.html.

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Figures (7)

Fig. 1.
Fig. 1.

SEM image of a layer of randomly packed polystyrene spheres (diameter 725nm) on dendrimeric molecules. (a) Particle solution concentration of 2.5% in weight per volume (w/v). (b) Particle solution concentration of 0.1% w/v. Inset: Fourier transform of the image presenting a ring representative of a uniform mean distance between beads.

Fig. 2.
Fig. 2.

Dense layer of randomly packed polystyrene spheres illuminated in transmission for different particle diameter d and filling factor η: (a) d=725nm, η=0.30; (b) d=725nm, η=0.40; (c) d=590nm, η=0.40; (d) d=508nm, η=0.40.

Fig. 3.
Fig. 3.

Specular transmission in the visible for dense layers of different particle diameters against size parameter x.

Fig. 4.
Fig. 4.

Comparison between experimental (solid line) and theoretical spectra for a dense layer (η=0.4) of 725nm polystyrene spheres. Theoretical data are calculated using SSA for a standard deviation of particle size σ=0nm (dotted line) and σ=20nm (dashed line).

Fig. 5.
Fig. 5.

Comparison between calculated (either using SSA or ISA) and experimental spectra of a randomly ordered layer of 725nm diameter polystyrene spheres for different filling factors.

Fig. 6.
Fig. 6.

Dependency of the observed color in transmission on the tilt angle φ: (a) φ=0°; (b) φ=45°.

Fig. 7.
Fig. 7.

Comparison between experimental and theoretical spectra for a dense layer (η=0.4) of 725nm diameter polystyrene spheres observed at 45°. Theoretical data are calculated using either SSA or MST. Inset: Polar diagram of the intensity scattered by a 725nm polystyrene sphere at λ=425nm (blue dashed line) and λ=775nm (red solid line). The forward direction is represented by an angle θ=0°.

Equations (8)

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I = E 2 = E 0 + N E s 2 = I 0 1 + N S ( 0 ) ikz exp [ ik ( x 2 + y 2 ) 2 z ] 2 ,
S ( 0 ) = 1 2 n = 1 ( 2 n + 1 ) ( a n + b n ) ,
T SSA = I I 0 = E 2 E 0 2 = 1 NS ( 0 ) 2 π k 2 2 .
T SSA = 1 4 η x 2 Re [ S ( 0 ) ] + 4 η 2 x 4 S ( 0 ) 2 .
T = 1 4 η x 2 Re [ S ( 0 ) ] = 1 NC SCA .
C SCA = π d 2 x 2 Re [ S ( 0 ) ] .
T MST = 1 4 η x 2 Re [ S ( 0 ) MST ] + 4 η 2 x 4 S ( 0 ) MST 2 ,
δ = 1 L λ = 400 800 T 1 , λ T 2 , λ ,

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